The two sides meet at the Kingpower Stadium this weekend.
They face a fight to do so though, as Claudio Ranieri’s side target a strong end to the season to secure the most unlikely of Premier League title wins.
The Hammers are currently without a win in three games, and Cottee expects that run to continue as he anticipates a draw against his old side.
“I think we have a chance of upsetting Leicester – if anyone can! It is going to be tough, but the one thing you could say is that if Leicester could pick a team not to play, it would probably be us.”
“We are capable of going there and getting a result,. I am confident we will get a goal, but it is whether we can stop them. I will go for a 1-1 draw.”
Slaven Bilic’s side could certainly do with a victory to give their Champions League hopes a boost.
They are currently sixth in the table and five points behind Manchester City in fourth, with their current winless run having dented their hopes of a top four finish.
With six games remaining though, there are plenty of points to play for though and a win over the would-be champions would provide them with a serious boost as the season draws to is conclusion.